A market/fair rate requires a market, something bigger than a single employer. If a market rate exists, it must be possible to pay someone above/below that rate. If the fair rate is always whatever someone is paid, the concepts of fair or market rates looses all meaning.
My understanding is that in a perfectly efficient free market, yes, everyone would be paid 'fair market rate' for their particular skills.
But such markets are only approximated in practice, and the interesting part of Economics is studying the effects of how actual markets differ from being perfectly free and efficient.
